Work in this thesis represents advances in addressing two key challenges in epidemiological and ecological modelling: the lack of an effective and easily deployable modelassessment tool and a statistically sound joint inferential framework for epidemic and evolutionary processes. Firstly, we present a novel statistical framework that combines classical and Bayesian reasoning in testing for mis-specifications of a spatiotemporal model by investigating the consistency of so-called latent residuals with a known sampling distribution using a classical hypothesis test. Second, we devise a statistically sound Bayesian framework which facilitates the integration of epidemiological and genetic data; specifically, we demonstrate how the transmitted sequences can be effectively imputed so that the transmission dynamics of the joint epidemic and evolution process can be accurately recovered and also any unsampled infected hosts can be naturally accommodated in the analysis. The new methodology we propose are assessed using simulation studies and they are applied to two real-world epidemic datasets which respectively describe the spread of an invasive plant and foot-andmouth disease in the UK, which shows that they may greatly enhance our ability to understand the transmission dynamics of disease and therefore lead to more efficient disease management.